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One of them says: 'The area swept out in a given time by the radius vector of the path of a planet is proportional to the time taken. From this I have to deduce that the force which confines the planet to its orbit is directed towards the sun. Gently entreated by the differential and integral calculus, already the formula is beginning to voice itself.
By examining the inequalities of the other planets he found that they all moved in elliptic orbits, and that the radius vector of each described areas proportional to the times. These two great results are known by the name of the first and second laws of Kepler.
Neither at Paris nor at Greenwich was any optical search undertaken; but Professor Airy wrote to ask M. Leverrier the same old question that he had fruitlessly put to Adams: Did the new theory explain the errors of the radius vector or not? The reply of Leverrier was both prompt and satisfactory these errors were explained, as well as all the others.
"They won't expect a ship to come in on that vector, steering away from the ports. Why should they? As far as I know it's never been tried since Terraport was laid out. It'll be tricky " And he himself would have to bear most of the responsibility for it. "But I believe that it can be done. And we can't just roam around out here.
Meanwhile Adams wrote to the astronomer-royal several additional communications, making improvements in his theory, and giving what he considered nearer and nearer approximations for the place of the planet. He also now answered quite satisfactorily, but too late, the question about the radius vector sent to him months before.
Would that scrap of information send some Patrolmen hurtling off to the Tower in search of the caged creature? The thought of such an expedition was, in a small way, comforting to the captives. An hour or so later they were fed, noiselessly and without visible attendants, when three trays slid through a slit in the wall at floor level. Rip's nose wrinkled. "Now I get the vector!
We junked all our boosters behind us on this take-off, and don't forget that, my friends." Weeks looked confused. "But I thought you said we could do this legal," he appealed to Rip. "If we're Patrol Posted as outlaws " "They can't do any more to us than they can for running in a plague ship," Ali pointed out. "Either will get us blasted if we happen into the wrong vector now. So what do we do?"
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